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Physics Beyond the Standard Model J. Hewett, ITEP Winter School 2010

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Why New Physics @ the Terascale? Electroweak Symmetry breaks at energies ~ 1 TeV (SM Higgs or ???) WW Scattering unitarized at energies ~ 1 TeV (SM Higgs or ???) Gauge Hierarchy: Nature is fine-tuned or Higgs mass must be stabilized by New Physics ~ 1 TeV Dark Matter: Weakly Interacting Massive Particle must have mass ~ 1 TeV to reproduce observed DM density All things point to the Terascale!

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A Revolution is Upon Us!

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Science Timeline: The Tools 2005 Tevatron 2020 20072010201220152018 LHC Upgrade LSST/JDEM ILC WMAP Auger Fermi PLANCK B-Factories Numi/Minos Super-K Kamland T2K/No a Underground & IndirectDark Matter Searches 0 LHCb

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Science Timeline: The Tools 2005 Tevatron 2020 20072010201220152018 LHC Upgrade LSST/JDEM ILC WMAP Auger Fermi PLANCK B-Factories Numi/Minos Super-K Kamland T2K/No a Underground & IndirectDark Matter Searches 0 LHCb

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The Standard Model Brief review of features which guide & restrict BSM physics

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The Standard Model of Particle Physics Symmetry: SU(3) C x SU(2) L x U(1) Y Building Blocks of Matter: QCDElectroweak Spontaneously Broken to QED This structure is experimentally confirmed!

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The Standard Model on One Page S Gauge = d 4 x F Y F Y + F F + F a F a S Fermions = d 4 x fDf S Higgs = d 4 x (D H) † (D H) – m 2 |H| 2 + |H| 4 S Yukawa = d 4 x Y u Qu c H + Y d Qd c H † + Y e Le c H † ( S Gravity = d 4 x g [M Pl 2 R + CC 4 ] ) Generationsf = Q,u,d, L,e

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Gauged Symmetries Q 3 2 +1/6 u c 3 1 -2/3 d c 3 1 +1/3 L 1 2 -1/2 e c 1 1 +1 Matter Fermions Color Electroweak SU(3) C x SU(2) L x U(1) Y

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Standard Model predictions well described by data! Pull EW measurements agree with SM predictions @ 2+ loop level Jet production rates @ Tevatron agree with QCD

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Search for the Higgs Boson: Direct Searches at LEP: m H > 114.4 GeV Indirect Searches at LEP/SLC: m H < 186 GeV @ 95% CL ZZ Higgs Z Tevatron Search

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Global Flavor Symmetries SM matter secretly has a large symmetry: Q 1 u 1 d 1 L 1 e 1.. 2.. 3 U(45) Rotate 45 fermions into each other U(3) Q x U(3) u x U(3) d x U(3) L x U(3) e U(1) B Baryon Number U(1) e x U(1) x U(1) Explicitly broken by gauging 3x2x1 Rotate among generations Explicitly broken by quark Yukawas + CKM Explicitly broken by charged lepton Yukawas U(1) L (Dirac) (or nothing) (Majorana) Explicitly broken by neutrino masses Lepton Number

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Global Symmetries of Higgs Sector Higgs Doublet: 1 + i 2 3 + i 4 Four real degrees of freedom Secretly transforms as a 12341234 4 of SO(4) (2,2) SU(2) x SU(2) SU(2) L of EW Left-over Global Symmetry Decomposes into subgroups

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Global Symmetries of Higgs Sector Higgs Doublet: 1 + i 2 3 + i 4 Four real degrees of freedom Secretly transforms as a 12341234 4 of SO(4) (2,2) SU(2) x SU(2) SU(2) L of EW Remaining Global Symmetry Decomposes into subgroups Gauging U(1) Y explicitly breaks Size of this breaking given by Hypercharge coupling g’ SU(2) Global Nothing M W 2 g 2 = 1 as g’ 0 M Z 2 g 2 + (g’) 2 New Physics may excessively break SU(2) Global Custodial Symmetry

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Standard Model Fermions are Chiral Fermions cannot simply ‘pair up’ to form mass terms i.e., mf L f R is forbidden -

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Standard Model Fermions are Chiral Fermions cannot simply ‘pair up’ to form mass terms i.e., mf L f R is forbidden Try it! (Qu c ) 1 2 -1/2 (Qd c ) 1 2 +1/2 (QL) 3 1 -1/3 (Qe) 3 2 +7/6 (u c d c ) 3x3 1 -1/3 (u c L) 3 2 -7/6 (u c e) 3 1 +1/3 (d c L) 3 2 -5/6 (d c e) 3 1 +4/3 (Le) 1 2 +1/2 - - SU(3) C SU(2) L U(1) Y - - - - - Fermion masses must be generated by Dimension-4 (Higgs) or higher operators to respect SM gauge invariance!

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Anomaly Cancellation Quantum violation of current conservation An anomaly leads to a mass for a gauge boson

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Anomaly Cancellation 3[ 2‧(1/6) – (2/3) + (1/3)] = 0 Q u c d c 3[3‧(1/6) – (1/2)] = 0 Q L 3[ 6‧(1/6) 3 + 3‧(-2/3) 3 + 3‧(1/3) 3 + 2‧(-1/2) 3 + 1 3 ] = 0 3[(1/6) – (2/3) + (1/3) – (1/2) +1] = 0 Q u c d c L e SU(3) SU(2) L U(1) Y g U(1) Y Can’t add any new fermion must be chiral or vector-like!

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Standard Model Summary Gauge Symmetry Flavor Symmetry Custodial Symmetry Chiral Fermions Gauge Anomalies SU(3) C x SU(2) L x U(1) Y ExactBroken to U(1) QED U(3) 5 U(1) B x U(1) L (?) Explicitly broken by Yukawas SU(2) Custodial of Higgs sector Broken by hypercharge so = 1 Need Higgs or Higher order operators Restrict quantum numbers of new fermions

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Standard Model Summary Gauge Symmetry Flavor Symmetry Custodial Symmetry Chiral Fermions Gauge Anomalies SU(3) C x SU(2) L x U(1) Y ExactBroken to U(1) QED U(3) 5 U(1) B x U(1) L (?) Explicitly broken by Yukawas SU(2) Custodial of Higgs sector Broken by hypercharge so = 1 Need Higgs or Higher order operators Restrict quantum numbers of new fermions Any model with New Physics must respect these symmetries

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Standard Model is an Effective field theory An effective field theory has a finite range of applicability in energy: Energy , Cutoff scale Particle masses All interactions consistent with gauged symmetries are permitted, including higher dimensional operators whose mass dimension is compensated for by powers of Theory is valid

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Constraints on Higher Dimensional Operators Baryon Number Violation Lepton Number Violation Flavor Violation CP Violation Precision Electroweak Contact Operators Generic Operators

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Gauge coupling unification: Our Telescope (GeV) 3030 4040 2020 1010 1 2 3 Counts charged matter Weak scale measurement High scale particle content

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Telescope to Unification Unification of Weak and Electromagnetic forces demonstrated at HERA ep collider at DESY Electroweak theory!

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Grand Unification 16 Gauge coupling unification indicates forces arise from single entity

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What sets the cutoff scale ? What is the theory above the cutoff? New Physics, Beyond the Standard Model! Three paradigms: 1.SM parameters are unnatural New physics introduced to “Naturalize” 2.SM gauge/matter content complicated New physics introduced to simplify 3.Deviation from SM observed in experiment New physics introduced to explain

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How unnatural are the SM parameters? Technically Natural –Fermion masses (Yukawa Couplings) –Gauge couplings –CKM Logarithmically sensitive to the cutoff scale Technically Unnatural Higgs mass Cosmological constant QCD vacuum angle Power-law sensitivity to the cutoff scale

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The naturalness problem that has had the greatest impact on collider physics is: The Higgs (mass) 2 problem or The hierarchy problem

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Do we really need a Higgs? Higgs Bad violation of unitarity A = a s/M W 2 + … Restores unitarity A = - a (s – m h 2 )/M W 2 + … Expand cross section into partial waves Unitarity bound (Optical theorem!) Gives m h < 4 M W LHC is designed to explore this entire region!

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The Hierarchy Energy (GeV) 10 19 10 16 10 3 10 -18 Solar System Gravity Weak GUT Planck desert Future Collider Energies All of known physics

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The Hierarchy Problem Energy (GeV) 10 19 10 16 10 3 10 -18 Solar System Gravity Weak GUT Planck desert Future Collider Energies All of known physics m H 2 ~~ M Pl 2 Quantum Corrections: Virtual Effects drag Weak Scale to M Pl

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Electroweak Hierarchy Problem Higgs (mass) 2 is quadratically divergent In the SM, m h is naturally ~ Λ, the largest energy scale m h ~ 100 GeV & Λ ~ M Pl ~ 10 19 GeV → cancellation in one part of 10 34

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A Cellar of New Ideas ’67 The Standard Model ’77 Vin de Technicolor ’70’s Supersymmetry: MSSM ’90’s SUSY Beyond MSSM ’90’s CP Violating Higgs ’98 Extra Dimensions ’02 Little Higgs ’03 Fat Higgs ’03 Higgsless ’04 Split Supersymmetry ’05 Twin Higgs a classic! aged to perfection better drink now mature, balanced, well developed - the Wino’s choice complex structure sleeper of the vintage what a surprise! svinters blend all upfront, no finish lacks symmetry young, still tannic needs to develop bold, peppery, spicy uncertain terrior J. Hewett finely-tuned double the taste

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Last Minute Model Building Anything Goes! Non-Communtative Geometries Return of the 4 th Generation Hidden Valleys Quirks – Macroscopic Strings Lee-Wick Field Theories Unparticle Physics ….. (We stilll have a bit more time)

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A Cellar of New Ideas ’67 The Standard Model ’77 Vin de Technicolor ’70’s Supersymmetry: MSSM ’90’s SUSY Beyond MSSM ’90’s CP Violating Higgs ’98 Extra Dimensions ’02 Little Higgs ’03 Fat Higgs ’03 Higgsless ’04 Split Supersymmetry ’05 Twin Higgs a classic! aged to perfection better drink now mature, balanced, well developed - the Wino’s choice complex structure sleeper of the vintage what a surprise! svinters blend all upfront, no finish lacks symmetry young, still tannic needs to develop bold, peppery, spicy uncertain terrior J. Hewett finely-tuned double the taste

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The Hierarchy Problem: Supersymmetry Energy (GeV) 10 19 10 16 10 3 10 -18 Solar System Gravity Weak GUT Planck desert Future Collider Energies All of known physics m H 2 ~~ M Pl 2 Quantum Corrections: Virtual Effects drag Weak Scale to M Pl m H 2 ~ ~ - M Pl 2 boson fermion Large virtual effects cancel order by order in perturbation theory

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Supersymmetry Supersymmetry is a new symmetry that relates fermions ↔ bosons

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Superpartners Translations: Particle P at point x → Particle P at point x’ Supersymmetry: Particle P at point x → Particle P at point x –P and P differ by spin ½: fermions ↔ bosons –P and P are identical in all other ways (mass, couplings….) ~ ~ ~ γγγ ~~

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Supersymmetry and Naturalness Dependence on Λ is softened to a logarithm SUSY solves hierarchy problem, if sparticle masses <1 TeV

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Supersymmetry: Recap Symmetry between fermions and bosons Predicts that every particle has a superpartner of equal mass Suppresses quantum effects Can make quantum mechanics consistent with gravity (with other ingredients)

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Supersymmetry : Recap Symmetry between fermions and bosons Predicts that every particle has a superpartner of equal mass ( SUSY is broken: many competing models!) Suppresses quantum effects Can make quantum mechanics consistent with gravity (with other ingredients)

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Higgs Doubling SUSY requires 2 Higgs doublets to cancel anomalies and to give mass to both up- and down-type particles Anomaly cancellation requires Σ Y 3 = 0, where Y is hypercharge and the sum is over all fermions SUSY adds an extra fermion with Y = -1 To cancel this anomaly, we add another Higgs doublet with Y = +1

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Supersymmetric Parameters

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Minimal Supersymmetric Standard Model Conserved multiplicative quantum number (R-parity) Superpartners are produced in pairs Heavier Superpartners decay to the Lightest Lightest Superpartner is stable Collider signatures dependent on this assumption and on model of SUSY breaking

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R-Parity: New Multiplicative Quantum Number One problem: proton decay! Forbid this with R-parity conservation: R p = (-1) 3(B-L)+2S –P has R p = +1; P has R p = -1 –Requires 2 superpartners in each interaction Consequence: the Lightest Supersymmetric Particle (LSP) is stable and cosmologically significant. What is the LSP? ~

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Neutral SUSY Particles

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Electroweak Symmetry Breaking

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Telescope to Unification Superpartners modify the scale dependence of couplings With TeV superpartners, the forces are unified! Unification scale ~ 10 16 GeV

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All parameters have scale dependence Superpartner mass determinations provide tests for unification Evolution of superpartner masses to high scale: Telescope to Unification

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SUSY Breaking SUSY is not an exact symmetry We don’t know how SUSY is broken, but SUSY breaking effects can be parameterized in the Lagrangian

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Parameterized SUSY Breaking There are over 100 parameters! Most of these are new flavor violation parameters or CP violating phases Causes difficulties in the flavor sector Need some simplifying assumptions

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SUSY Effects in FCNC Super-GIM mechanism Must be Flavor Universal Couplings Scalar Masses Trilinear A-Terms Scalar particles are approximately degenerate!

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Mediation of SUSY Breaking Weak Scale MSSM Susy Breaking Hidden Sector Mediation SUSY breaking occurs through interactions of Intermediate particles Theoretical assumptions @ the GUT scale reduce the number of parameters 3 Popular SUSY breaking scenarios: Gravity Mediation (mSUGRA) Gauge Mediation Anomaly Mediation

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Gravity Mediated SUSY Breaking (mSUGRA)

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Two MSSM Model Frameworks The constrained MSSM (CMSSM) –Based on mSUGRA –Common masses & couplings at the GUT scale –m 0, m 1/2, A 0, tanβ = v 2 /v 1, sign μ The phenomenological MSSM (pMSSM) –19 real, weak-scale parameters scalars: m Q 1, m Q 3, m u 1, m d 1, m u 3, m d 3, m L 1, m L 3, m e 1, m e 3 gauginos: M 1, M 2, M 3 tri-linear couplings: A b, A t, A τ Higgs/Higgsino: μ, M A, tanβ

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Predictions for Lightest Higgs Mass in the CMSSM Framework CMSSM: m 0, m 1/2, A 0, tanβ, sign μ Χ 2 fit to some global data set Fit to EW precision, B-physics observables, & WMAP Ellis etal arXiv:0706.0652

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Predictions for Lightest Higgs Mass in the pMSSM Berger, Gainer, JLH, Rizzo 0812.0980 Models consistent with EW Precision, B Physics, Cosmology, and Collider data

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Squarks & Gluinos @ the Tevatron mSUGRA limits

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Gluinos at the Tevatron Tevatron gluino/squark analyses performed for mSUGRA – constant ratio m gluino : m Bino ≃ 6 : 1 Gluino-Bino mass ratio determines kinematics x Distribution of Gluino Masses Berger, Gainer, JLH, Rizzo 0812.0980

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Supersymmetry at the LHC Sparticle mass (GeV) Production cross section (pb)

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Supersymmetry at the LHC SUSY discovery generally ‘easy’ at LHC: Multijets + missing E T

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LHC mSUGRA Discovery Reach (14 TeV)

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Sample pMSSM Results Conley, Gainer, JLH, Le, Rizzo In progress 14 TeV, 1 fb -1

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SUSY Mass Scale from Inclusive Analysis

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Reconstruction of Sparticle Masses at LHC Main analysis tool : dilepton edge i n 0 2 0 1 l + l - Proportional to Sparticle mass differences Introduces strong mass correlations Squarks and Gluinos have complicated decay chains

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The ATLAS SUSY analyses: 2,3,4-jet +MET 1l, ≥4-jet +MET Same Sign Di-Lepton Opposite Sign Di-Lepton Trileptons + (0,1)-j +MET +≥ 4j +MET ≥4j w/ ≥ 2btags + MET Stable particle search

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Some Results From 70k pMSSM Models * * ID & reconstruction in PGS is a bit too optimistic & needs to be reaccessed Conley, Gainer, JLH, Le, Rizzo In progress

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ILC Studies superpartners individually via e + e - SS Determines Quantum numbers (spin!) Supersymmetric relation of couplings = e ~ ~ = 2e - Proof that it IS Supersymmetry! Supersymmetry at the ILC M 1 (GeV) Ratio of Coupling Stregths Selectron pair production 2% accuracy in determination of Supersymmetric coupling strength

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Precise Mass Measurements of Superpartners Example: e e + Fixed center of mass energy gives flat energy distribution in the laboratory for final state e - Endpoints can be used to determine superpartner masses to part-per-mil accuracy ~~ e A realistic simulation: Determines Superpartner masses of the electron and photon to 0.05%

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SUSY parameter determination: Fittino SPS1a’ Bechtle, Desch, Wienemann, hep-ph/0506244 Precise determination of parameters only possible with LHC + ILC Reconstruction of SUSY Lagrangian (without assumptions) becomes possible!

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Dark Matter Candidates The observational constraints are no match for the creativity of theorists Masses and interaction strengths span many, many orders of magnitude, but not all candidates are equally motivated Weakly Interacting Massive Particle (WIMP) HEPAP/AAAC DMSAG Subpanel (2007) SUSY

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The WIMP ‘Miracle ’ (1)Assume a new (heavy) particle is initially in thermal equilibrium : ↔ f f (2) Universe cools: f f (3) s “freeze out”: f f (1) (2) (3) → ← / → ← / / Zeldovich et al. (1960s)

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The amount of dark matter left over is inversely proportional to the annihilation cross section: DM ~ Remarkable “coincidence”: DM ~ 0.1 for m ~ 100 GeV – 1 TeV WIMP! particle physics independently predicts particles with about the right density to be dark matter ! HEPAP LHC/ILC Subpanel (2006) [band width from k = 0.5 – 2, S and P wave] A ~ 2 / m 2

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Relic Density: Neutralino LSP

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Contributions to Neutralino WIMP Annihilation

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Cosmologically Preferred SUSY: mSUGRA

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Relic Density Determinations

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Identifying Dark Matter J. Feng

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Dark Matter Detection photons, positrons, anti-protons…. ‘in the sky’ right now may be seen by PAMELA, FERMI & other experiments N N (elastic) scattering may be detected on earth in deep underground experiments If is really a WIMP it may be directly produced at the LHC !

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Direct Detection Prospects mSUGRApMSSM Berger, Gainer, JLH, Rizzo 0812.0980

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Supersymmetry Summary SUSY solves many questions: –Gauge hierarchy –EWSB –Gauge coupling unification –Dark Matter candidate SUSY has some issues: –120 free parameters –In most natural case, we would have discovered it already –Has problems fitting indirect DM search data (PAMELA, Fermi) LHC will tell us if SUSY is relevant to the weak scale or not! (If the signal isn’t missed….)

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Extra Dimensions Taxonomy Large TeV Small FlatCurved UEDs RS Models GUT Models ADD Models

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Extra dimensions can be difficult to visualize 3-dimensional shadow of a rotating hypercube 2-dimensional shadow of a rotating cube One picture: shadows of higher dimensional objects

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Extra dimensions can be difficult to visualize Another picture: extra dimensions are too small for us to observe they are ‘curled up’ and compact The tightrope walker only sees one dimension: back & forth. The ants see two dimensions: back & forth and around the circle

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Every point in spacetime has curled up extra dimensions associated with it One extra dimension is a circle Two extra dimensions can be represented by a sphere Six extra dimensions can be represented by a Calabi-Yau space

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The Braneworld Scenario Yet another picture We are trapped on a 3-dimensional spatial membrane and cannot move in the extra dimensions Gravity spreads out and moves in the extra space The extra dimensions can be either very small or very large

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Are Extra Dimensions Compact? QM tells us that the momentum of a particle traveling along an infinite dimension takes a continuous set of eigenvalues. So, if ED are not compact, SM fields must be confined to 4D OTHERWISE we would observe states with a continuum of mass values. If ED are compact (of finite size L), then QM tells us that p 5 takes on quantized values (n/L). Collider experiments tell us that SM particles can only live in ED if 1/L > a few 100 GeV.

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Kaluza-Klein tower of particles E 2 = (p x c) 2 + (p y c) 2 + (p z c) 2 + (p extra c) 2 + (mc 2 ) 2 In 4 dimensions, looks like a mass! Recall p extra = n/R Small radiusLarge radius Tower of massive particles

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Kaluza-Klein tower of particles E 2 = (p x c) 2 + (p y c) 2 + (p z c) 2 + (p extra c) 2 + (mc 2 ) 2 In 4 dimensions, looks like a mass! Recall p extra = n/R Small radiusLarge radius Small radius gives well separated Kaluza-Klein particles Large radius gives finely separated Kaluza- Klein particles Tower of massive particles

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Action Approach: Consider a real, massless scalar in flat 5-d

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Masses of KK modes are determined by the interval BC

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Time-like or Space-like Extra Dimensions ? Consider a massless particle, p 2 =0, moving in flat 5-d Then p 2 = 0 = p μ p μ ± p 5 2 If the + sign is chosen, the extra dimension is time-like, then in 4-d we would interpret p 5 2 as a tachyonic mass term, leading to violations of causality Thus extra dimensions are usually considered to be space-like

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Higher Dimensional Field Decomposition As we saw, 5-d scalar becomes a 4-d tower of scalars Recall: Lorentz (4-d) ↔ Rotations (3-d) scalar scalar 4-vector A μ A, Φ tensor F μν E, B 5-d: 5-d ↔ 4-d scalar (scalar) n vector A M (A μ, A 5 ) n tensor h MN (h μν, h μ5, h 55 ) n KK towers → →→

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Higher Dimensional Field Decomposition As we saw, 5-d scalar becomes a 4-d tower of scalars Recall: Lorentz (4-d) ↔ Rotations (3-d) scalar scalar 4-vector A μ A, Φ tensor F μν E, B 4+δ-d: 4+δ-d ↔ 4-d (i=1…δ) scalar (δ scalars) n vector A M (A μ, A i ) ni tensor h MN (h μν, h μi, h ij ) n KK towers 1 tensor, δ 4-vectors, ½ δ(δ+1) scalars → →→

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Experimental observation of KK states: Signals evidence of extra dimensions Properties of KK states : Determined by geometry of extra dimensions Measured by experiment! The physics of extra dimensions is the physics of the KK excitations

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What are extra dimensions good for? Can unify the forces Can explain why gravity is weak (solve hierarchy problem) Can break the electroweak force Contain Dark Matter Candidates Can generate neutrino masses …… Extra dimensions can do everything SUSY can do!

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If observed: Things we will want to know How many extra dimensions are there? How big are they? What is their shape? What particles feel their presence? Do we live on a membrane? …

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If observed: Things we will want to know How many extra dimensions are there? How big are they? What is their shape? What particles feel their presence? Do we live on a membrane? … Can we park in extra dimensions? When doing laundry, is that where all the socks go?

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Searches for extra dimensions Three ways we hope to see extra dimensions: 1.Modifications of gravity at short distances 1.Effects of Kaluza-Klein particles on astrophysical/cosmological processes 1.Observation of Kaluza-Klein particles in high energy accelerators

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The Hierarchy Problem: Extra Dimensions Energy (GeV) 10 19 10 16 10 3 10 -18 Solar System Gravity Weak – Quantum Gravity GUT Planck desert Future Collider Energies All of known physics Simplest Model: Large Extra Dimensions = Fundamental scale in 4 + dimensions M Pl 2 = (Volume) M D 2+ Gravity propagates in D = 3+1 + dimensions

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Large Extra Dimensions Motivation: solve the hierarchy problem by removing it! SM fields confined to 3-brane Gravity becomes strong in the bulk Arkani-Hamed, Dimopoulos, Dvali, SLAC-PUB-7801 Gauss’ Law: M Pl 2 = V M D 2+ , V = R c M D = Fundamental scale in the bulk ~ TeV

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Constraints from Cavendish-type exp’ts

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Constraints from Astrophysics/Cosmology Supernova Cooling NN NN + G n can cool supernova too rapidly Cosmic Diffuse Rays NN NN + G n G n Matter Dominated Universe too many KK states Neutron Star Heat Excess NN NN + G n becomes trapped in neutron star halo and heats it - Cullen, Perelstein Barger etal, Savage etal Hannestad, Raffelt Hall, Smith Fairbairn Hannestad, Raffelt

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Bulk Metric: Linearized Quantum Gravity Perform Graviton KK reduction Expand h AB into KK tower SM on 3-brane Set T = A B (y a ) Pick a gauge Integrate over d y Interactions of Graviton KK states with SM fields on 3-brane

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Feyman Rules: Graviton KK Tower Han, Lykken, Zhang; Giudice, Rattazzi, Wells Massless 0-mode + KK states have indentical coupling to matter

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Collider Tests

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Graviton Tower Exchange: XX G n YY Search for 1) Deviations in SM processes 2) New processes! (gg ℓℓ) Angular distributions reveal spin-2 exchange G n are densely packed! ( s R c ) states are exchanged! (~10 30 for =2 and s = 1 TeV) Giudice, Rattazzi, Wells JLH M

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Drell-Yan Spectrum @ LHC Forward-Backward Asymmetry JLH M D = 2.5 TeV 4.0 Graviton Exchange

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Graviton Exchange @ 7 TeV LHC

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Issue: How to determine spin of exchanged particle?

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Graviton Tower Emission e + e - /Z + G n G n appears as missing energy qq g + G n Model independent – Probes M D directly Z ff + G n Sensitive to Parameterized by density of states: Discovery reach for M D (TeV): - - Giudice, Ratazzi,Wells Mirabelli,Perelstein,Peskin

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Graviton Emission @ LHC

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Graviton Emission @ LHC @ 7 TeV

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Detailed LHC/ATLAS MC Study The 14 TeV LHC is seen to have considerable search reach for KK Graviton production Hinchliffe, Vacavant

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Current Bounds on Graviton Emission

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BEWARE! There is a subtlety in this calculation When integrating over the kinematics, we enter a region where the collision energies EXCEED the 4+n-dimensional Planck scale This region requires Quantum Gravity or a UV completion to the ADD model There are ways to handle this, which result in minor modifications to the spectrum at large E T that may be observable

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Graviton Emission in e + e - Collisions Giudice, Rattazzi, Wells

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Black Hole Production @ LHC: Black Holes produced when s > M D Classical Approximation: [space curvature << E] E/2 b b < R s (E) BH forms M BH ~ s ^ Geometric Considerations: Naïve = F n R s 2 (E), details show this holds up to a factor of a few Dimopoulos, Landsberg Giddings, Thomas

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Blackhole Formation Factor

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Potential Corrections to Classical Approximation 1.Distortions from finite R c as R s R c 2. Quantum Gravity Effects Higher curvature term corrections Critical point for instabilities for n=5: (R s /R c ) 2 ~ 0.1 @ LHC Gauss-Bonnet term R S 2 /(2 R c ) 2 n = 2 - 20 n 2 ≤ 1 in string models

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Production rate is enormous! 1 per sec at LHC! Naïve ~ n for large n M D = 1.5 TeV JLH, Lillie, Rizzo

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Cosmic Ray Sensitivity to Black Hole Production Ringwald, Tu Anchordoqui etal No suppression

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Summary of Exp’t Constraints on M D Anchordoqui, Feng Goldberg, Shapere

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Black Hole Decay Balding phase: loses ‘hair’ and multiple moments by gravitational radiation Spin-down phase: loses angular momentum by Hawking radiation Schwarzschild phase: loses mass by Hawking radiation – radiates all SM particles Planck phase: final decay or stable remnant determined by quantum gravity

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Decay Properties of Black Holes (after Balding): Decay proceeds by thermal emission of Hawking radiation At fixed M BH, higher dimensional BH’s are hotter: N ~ 1/ T higher dimensional BH’s emit fewer quanta, with each quanta having higher energy Harris etal hep-ph/0411022 Multiplicity for n = 2 to n = 6 Not very sensitive to BH rotation for n > 1

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Grey-body Factors Particle multiplicity in decay: = grey-body factor Contain energy & anglular emission information

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p T distributions of Black Hole decays Provide good discriminating power for value of n Generated using modified CHARYBDIS linked to PYTHIA with M * = 1 TeV

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Black Hole event simulation @ LHC

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LED: Is the hierarchy problem really solved? M * R c > 10 8 for n = 2-6 Disparate values for gravity and EWK scales traded for disparate values of M * and R c However, 1 < M * R c < 10 for n = 17 - 40 Large n offers true solution to hierarchy!

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Collider Signatures Change with large n Graviton KK states are now ‘invisible’ m 1 ~ TeV Couplings are still M Pl -1 Collider searches are highly degraded! For n = 2, M * up to 10 TeV observable at ILC, LHC Drops to < 1 TeV for n = 20 Only viable collider signature is Black Hole production!

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Questions you might ask about LED: Doesn’t string/M-theory fix = 6,7? Aren’t there string-inspired models where SM gauge fields have KK excitations? Do all dimensions have to be the same size?

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Flat TeV -1 –size Extra Dimensions Can arise naturally in string-inspired models The Standard Model goes into the bulk! Model building choices: Gauge fields in the bulk Higgs in the bulk or on the brane? Fermions: –Located at orbifold fixed points –Localized to specific points inside the bulk (Split Fermions) –Freely propagate inside the bulk (Universal Extra Dimensions) Antoniadis

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Orbifolding in 1 Extra Dimension y

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Aside: Double Orbifolds!

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Precision Electroweak Data (fermions @ fixed points) Exchange of gauge KK excitations contribute to precision EW observables Contributions include: –Tree-level KK interactions (e.g., decay) –KK – zero mode mixing (e.g., affects Z-pole observables) –Zero mode loop corrections KK tower exchanges induce new dim-6 operators with coefficients Perform full fit to global precision EW data set Bound on compactification scale, degrades to M c > 2-3 TeV for localized fermions M c > 4.5 TeV Rizzo, Wells Delgado, Pomerol

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Searches @ Colliders (fermions @ fixed points) Hadron Colliders: Drell-Yan /Z/W KK resonance dijet g KK resonance –qq n /Z n ℓℓ –qq W n ℓ –qq,gg g n jj e + e - Colliders: Indirect search in e + e - n /Z n ff Observe deviation from SM Fit to f, A FB f, A LR f, A pol Bumps! Tevatron Run I: M c > 0.8 TeV Run II M c > 1.1 TeV - - - -

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Even spacing denotes flat space m 2 = 2m 1 KK /Z Production @ LHC, M c = 4 TeV D = separation of fermions in 5 th dimension

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ATLAS Simulation for /Z KK Production Azuelos, Polesello Les Houches 01 Discovery Reach: M c < 6.3 TeV

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KK gluon dijet mass bumps @ LHC

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Localized Fermions in Extra Dimension Arkani-Hamed, Schmaltz kink y f for each fermion. Overlap of Left- & Right-handed wavefunctions give Yukawa couplings!

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Proton Decay

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Exponential Fall-off of Scattering Cross Sections If collision energy is high enough, the two interacting partons will probe separation distance between them! Exponential fall-off of cross section for fermion pair production Arkani-Hamed, Grossman, Schmaltz Energy (TeV) / SM for pair production

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Universal Extra Dimensions All SM fields in TeV -1, 5d, S 1 /Z 2 bulk No branes! translational invariance is preserved tree-level conservation of p 5 KK number conserved at tree-level broken at higher order by boundary terms KK parity conserved to all orders, (-1) n Consequences: 1.KK excitations only produced in pairs Relaxation of collider & precision EW constraints R c -1 ≥ 300 GeV! 2.Lightest KK particle is stable (LKP) and is Dark Matter candidate 3.Boundary terms separate masses and give SUSY-like spectrum Appelquist, Cheng, Dobrescu

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Universal Extra Dimensions: Bosonic SUSY Phenomenology looks like Supersymmetry: Heavier particles cascade down to LKP LKP: Photon KK state appears as missing E T SUSY-like Spectroscopy Confusion with SUSY if discovered @ LHC ! Chang, Matchev,Schmaltz Spectrum looks like SUSY !

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How to distinguish SUSY from UED I: Observe KK states in e + e - annihilation Measure their spin via: Threshold production, s-wave vs p-wave Distribution of decay products However, could require CLIC energies... JLH, Rizzo, Tait Datta, Kong, Matchev

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How to distinguish SUSY from UED II: Observe higher level (n = 2) KK states: –Pair production of q 2 q 2, q 2 g 2, V 2 V 2 –Single production of V 2 via (1) small KK number breaking couplings and (2) from cascade decays of q 2 Discovery reach @ LHC Datta, Kong, Matchev

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How to distinguish SUSY from UED III: Measure the spins of the KK states @ LHC – Difficult! Decay chains in SUSY and UED: Form charge asymmetry: Works for some, but not all, regions of parameter space Smillie, Webber

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UED Dark Matter Candidate: 1 Calculate relic density from 1 annihilation and co-annihiliation WMAP Kong, Matchev Tait, Servant

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LED: Is the hierarchy problem really solved? M * R c > 10 8 for n = 2-6 Disparate values for gravity and EWK scales traded for disparate values of M * and R c However, 1 < M * R c < 10 for n = 17 - 40 Large n offers true solution to hierarchy!

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Flat TeV -1 –size Extra Dimensions Can arise naturally in string-inspired models The Standard Model goes into the bulk! Model building choices: Gauge fields in the bulk Higgs in the bulk or on the brane? Fermions: –Located at orbifold fixed points –Localized to specific points inside the bulk (Split Fermions) –Freely propagate inside the bulk (Universal Extra Dimensions) Antoniadis

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Orbifolding in 1 Extra Dimension y

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ATLAS Simulation for /Z KK Production Azuelos, Polesello Les Houches 01 Discovery Reach: M c < 6.3 TeV

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The Hierarchy Problem: Extra Dimensions Energy (GeV) 10 19 10 16 10 3 10 -18 Solar System Gravity Weak GUT Planck desert Future Collider Energies All of known physics Model II: Warped Extra Dimensions wk = M Pl e -kr strong curvature

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Non-Factorizable Curved Geometry: Warped Space Area of each grid is equal Field lines spread out faster with more volume Drop to bottom brane Gravity appears weak on top brane!

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Localized Gravity: Warped Extra Dimensions Randall, Sundrum Bulk = Slice of AdS 5 5 = -24M 5 3 k 2 k = curvature scale Naturally stablized via Goldberger-Wise Hierarchy is generated by exponential!

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4-d Effective Theory Phenomenology governed by two parameters: ~ TeV k/M Pl ≲ 0.1 5-d curvature: |R 5 | = 20k 2 < M 5 2 Davoudiasl, JLH, Rizzo

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Interactions Recall = M Pl e k r ~ TeV

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Randall-Sundrum Graviton KK spectrum e + e - + - Davoudiasl, JLH, Rizzo Unequal spacing signals curved space Different curves for k/M Pl =0.01 – 1.0 LHC pp → l + l - e + e - →μ + μ -

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Tevatron limits on RS Gravitons CDF Drell-Yan spectrum

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Summary of Theory & Experimental Constraints LHC can cover entire allowed parameter space!!

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Graviton Branching Fractions B = 2B ℓℓ

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Measuring Graviton KK Properties Davoudiasl, JLH, Rizzo n=1,2 KK Graviton productionSpin determination

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Extend Manifold: AdS 5 x S e + e - + - Drell-Yan Davoudiasl, JLH, Rizzo Gives a forest of KK graviton resonances!

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Problem with Higher Dimensional Operators Recall the higher dimensional operators that mediate proton decay & FCNC These are supposed to be suppressed by some high mass scale But all high mass scales present in any RS Lagrangian are warped down to the TeV scale. ⇒ There is no mechanism to suppress these dangerous operators! Could employ discrete symmetries ala SUSY – but there is a more elegant solution….

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Peeling the Standard Model off the Brane Model building scenarios require SM bulk fields –Gauge coupling unification –Supersymmetry breaking – mass generation –Fermion mass hierarchy –Suppression of higher dimensional operators Gauge boson KK towers have coupling g KK = 8.4g SM Precision EW Data Constrains: m 1 A > 25 TeV > 100 TeV! SM gauge fields alone in the bulk violate custodial symmetry Davoudiasl, JLH, Rizzo Pomarol Start with gauge fields in the bulk:

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Derivation of Bulk Gauge KK Spectrum

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Add Fermions in the Bulk Each SM chiral fermion has a double KK tower of fermions associated with it of both helicities Introduces new parameter, related to fermion Yukawa –m f bulk = k, with ~ O(1) KK Spectra are related: Grossman, Neubert Ghergetta, Pomarol Davoudiasl, JLH, Rizzo

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Add Fermions in the Bulk Zero-mode fermions couple weaker to gauge KK states than brane fermions Precision EW Constraints towards Planck brane towards TeV brane

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Schematic of Wavefunctions Planck braneTeV brane Can reproduce Fermion mass hierarchy

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Collider Signals are more difficult gg G n ZZ gg g n tt Agashe, Davoudiasl, Perez, Soni hep-ph/0701186 - Lillie, Randall, Wang, hep-ph/0701164 KK states must couple to gauge fields or top-quark to be produced at observable rates

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The Hierarchy Problem: Higgsless Energy (GeV) 10 19 10 16 10 3 10 -18 Solar System Gravity Weak GUT Planck desert Future Collider Energies All of known physics Warped Extra Dimensions wk = M Pl e -kr With NO Higgs boson! strong curvature

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Higgsless EWSB What good is a Higgs anyway?? Generates W,Z Masses Generates fermion Masses Unitarizes scattering amplitudes (W L W L W L W L ) Do we really need a Higgs? And get everything we know right…. Our laboratory: Standard Model in 1 extra warped dimension Minimal Particle Content! Csaki, Grojean,Murayama, Pilo, Terning

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Generating Masses Consider a massless 5-d field ∂ 2 = (∂ ∂ - ∂ 5 ∂ 5 ) = 0 looks like (∂ ∂ - m n 2 ) = 0 in 4-d (KK tower) The curvature of the 5-d wavefunction (y) is related to its mass in 4-d

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Toy Example: Flat space with U(1) gauge field in bulk with S 1 /Z 2 Orbifold A (y) ~ cos (ny/R) A 5 (y) ~ sin (ny/R) 0 RR 0-mode 1 st KK 0-mode is flat & y independent m 0 = 0 If The Same boundary conditions are applied at both boundaries, 0-mode is massless and U(1) remains unbroken

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A(y) ~ n a n cos(m n y) + b n sin(m n y) ∂ 5 A(y) ~ m n n (-a n sin(m n y) + b n cos(m n y) BC’s: A(y=0) = 0 a n = 0 ∂ 5 A(y= R) = 0 cos(m n R) = 0 ∂ 5 A =0 A =0 1 st KK 0-mode A cannot be flat with these boundary conditions! m n = (n + ½)/R The zero mode is massive! A 5 acts as a Goldstone U(1) is broken Orbifold Boundary Conditions: ∂ 5 A = 0 A 5 = 0

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Realistic Framework: SU(2) L x SU(2) R x U(1) B-L in 5-d Warped bulk Agashe etal hep-ph/0308036 Csaki etal hep-ph/0308038 Planck brane TeV-brane SU(2) R x U(1) B-L U(1) Y SU(2) L x SU(2) R SU(2) D SU(2) Custodial Symmetry is preserved! W R , Z R get Planck scale masses W , Z get TeV scale masses left massless! BC’s restricted by variation of the action at boundary Parameters: = g 5R /g 5L (restricted range) L,Y,B,D brane kinetic terms g 5L fixed by G F, g 5B /g 5L fixed by M Z

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Exchange gauge KK towers: Conditions on KK masses & couplings: (g 1111 ) 2 = k (g 11k ) 2 4(g 1111 ) 2 M 1 2 = k (g 11k ) 2 M k 2 Necessary, but not sufficient, to guarantee perturbative unitarity! Csaki etal, hep-ph/0305237 Unitarity in Gauge Boson Scattering SM without Higgs violates perturbative unitarity in W L W L W L W L at s ~ 1.7 TeV Higgs restores unitarity if m H < TeV What do we do without a Higgs??

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Production of Gauge KK States @ LHC gg, qq g 1 dijets - Davoudiasl, JLH, Lilllie, RizzoBalyaev, Christensen

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What are the preferred gauge KK masses? Tension Headache : Colliders PUV in WW scattering Precision EW needs light KK’s needs heavier KK’s Important direct constraints Is there a consistent region of parameter space?

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What are the preferred gauge KK masses? Tension Headache : Colliders PUV in WW scattering Precision EW needs light KK’s needs heavier KK’s Important direct constraints Is there a consistent region of parameter space? Only if fermions are in the bulk at specific locations

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Summary of Extra Dimensions Many models of extra dimensions exist! Extra dimensions were founded to resolve the hierarchy, but now stand on their own for answering many open questions of the Standard Model Extra dimensions which resolve the gauge hierarchy are testable at the LHC/ILC. These models can be proved or disproved regarding their relevance to the hierarchy If discovered, collider measurements can reveal many properties of extra dimensions If discovered, our view of the universe will be forever changed.

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The Hierarchy Problem: Little Higgs Energy (GeV) 10 19 10 16 10 3 10 -18 Solar System Gravity Weak GUT Planck desert Future Collider Energies All of known physics Little Hierarchies! 10 4 New Physics! Simplest Model: The Littlest Higgs with ~ 10 TeV No UV completion

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The Hierarchy Problem: Little Higgs Energy (GeV) 10 19 10 16 10 3 10 -18 Solar System Gravity Weak GUT Planck Future Collider Energies All of known physics Stacks of Little Hierarchies 10 4 New Physics! Simplest Model: The Littlest Higgs with 1 ~ 10 TeV 2 ~ 100 TeV 3 ~ 1000 TeV ….. 10 5 10 6...... New Physics!

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Little Higgs: The Basics The Higgs becomes a component of a larger multiplet of scalars, transforms non-linearly under a new global symmetry New global symmetry undergoes SSB leaves Higgs as goldstone Part of global symmetry is gauged Higgs is pseudo-goldstone Careful gauging removes Higgs 1-loop divergences 2 m h 2 ~, > 10 TeV, @ 2-loops! (16 2 ) 2

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Minimal Model: The Littlest Higgs > 10 TeV : non-linear model is strongly-coupled 10 TeV: Global Symmetry: SU(5) SO(5) via SSB with 0 (x) = e 2i /f 0, = a a (x)X a 14 Goldstone Bosons f ~ /4 = G.B. decay constant ~ TeV Gauged Symmetry: G 1 x G 2 [SU(2) x U(1)] 2 SU(2) L x U(1) Y via SSB with 0 W H , Z H, B H acquire mass ~ f W , W 3 0, B 0 remain massless 14 Goldstone Bosons 4 eaten under SSB complex triplet complex doublet h Acquires mass at 1-lopp via gauge interactions ~ f h acquires mass at 2-loops ~ f/4 Arkani-Hamed, Cohen, Katz, Nelson massless at tree-level

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3-Scale Model > 10 TeV: New Strong Dynamics Global Symmetry f ~ /4 ~ TeV: Symmetires Broken Pseudo-Goldstone Scalars New Gauge Fields New Fermions v ~ f/4 ~ 100 GeV: Light Higgs SM vector bosons & fermions ? UV Completion ? Sample Spectrum

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A UV Completion Keep stacking Little Higgs Theories Upstairs Little Higgs: Strongly coupled @ ~ 100 TeV non-linear model symmetry breaks @ F ~ 10 TeV Downstairs Little Higgs: Weakly coupled @ ~ 10 TeV linear model symmetry breaks @ f ~ 1 TeV Kaplan, Schmaltz, Skiba

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Summary of Physics Beyond the Standard Model There are many ideas for scenarios with new physics! Most of our thinking has been guided by the hierarchy problem They must obey the symmetries of the SM They are testable at the LHC We are as ready for the LHC as we will ever be The most likely scenario to be discovered at the LHC is the one we haven’t thought of yet. Exciting times are about to begin. Be prepared for the unexpected!!

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Fine-tuning does occur in nature 2001 solar eclipse as viewed from Africa

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Most Likely Scenario @ LHC: H. Murayama

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